For using it you only need to place lua libs in your library path and setup all the header files of lua needed to use the lua C api.
When you're done you can directly execute char* buffers of code with luaL_dostring(...) or (much more effective and correct) using c api. Since lua has a stackable engine you should add operation to the stack pointer. There are a lots of manual about that on internet, official lua page, or this forum.
In addition, you are able to use this tool to figure out how this stack works. You can place your lua code and press "lua2c", that will dump the equivalent c api code.
For example
a=1
b="a"
c=true
myvariable=functionname(a,b,{c,a})
static int MAIN(lua_State *L)
{
lua_pushnumber(L,1);
lua_setglobal(L,"a");
lua_pushstring(L,"a");
lua_setglobal(L,"b");
lua_getglobal(L,"true");
lua_setglobal(L,"c");
lua_getglobal(L,"functionname");
lua_getglobal(L,"a");
lua_getglobal(L,"b");
lua_newtable(L);
lua_getglobal(L,"c");
lua_getglobal(L,"a");
lua_rawseti(L,-3,2);
lua_rawseti(L,-2,1);
lua_call(L,3,1);
lua_setglobal(L,"myvariable");
return 0;
}